Securities portfolio transactions typically incur transaction costs arising not only from commissions and bid-offer spreads, but also from price movements (market impact) associated with execution. Execution costs can be large, especially when compared against gross returns, and might substantially reduce or even eliminate the notional returns to a particular investment strategy.1 A large body of research (Keim and Madhavan (1998) provide a survey) shows that market or price impact is a major component of total trading cost. Consequently, minimization of transaction costs has been a long-standing aim, especially for traders handling portfolio transactions; e.g., transactions that rebalance securities positions in a portfolio over a specified period of time. A related goal is to develop optimal trading strategies to minimize trading costs or some other objective criterion. For an equally weighted global portfolio of stocks, turned over twice a year, such costs alone account for 23 percent of returns over recent history. See Domowitz, Glen, and Madhavan, “Liquidity, Volatility, and Equity Trading Costs Across Countries and Over Time,” working paper, Pennsylvania State University, January, (2001) for discussion, analysis, and precise definitions of cost.
To this end, statistical and mathematical models have been developed in an attempt to forecast the transaction costs of a proposed portfolio trade execution. These models typically build on some known empirical facts about trading costs. For example, empirical studies have established that costs increase in trade difficulty, a factor systematically related to order size (relative to average trading volumes), venue (e.g., Exchange Listed Trades vs. Over The Counter (“OTC”)), trade direction (Buys vs. Sells), firm size (Market Capitalization), Risk (e.g., the volatility of security returns), and price level. In addition, costs are also systematically related to trading style, as reported by Keim and Madhavan (1998). Traders who trade passively (using limit orders and spreading their trades over a long period of time) incur lower costs, on average, than traders who trade more aggressively using market orders to demand immediacy. Two otherwise identical orders might have very different trading costs depending on how a trader presents them to the market. See Madhavan (2000) for details.
Of the many statistical and mathematical forecasting models developed, most suffer from the inability to perform comprehensive analyses of transaction costs because the level of trade difficulty and the impact of trading style (e.g., horizon over which trading takes place) is not analyzed or not accurately analyzed. Therefore, there is a need in the field to include in a forecasting model an adjustment factor that accurately accounts for trade difficulty and market conditions, allowing for a valid comparison of trades executed in different circumstances and trading conditions. It is important that this system accommodate parameters for trading style. Since the trader's style is closely related to their ultimate objectives (e.g., a value trader might trade passively over several days to minimize price impact costs, tolerating the risk of adverse price movements in the interim), this creates a need for a model that ties strategy to a trader's subjective assessment of risk. In particular, there is a need in the field to provide a model that would recommend an optimal trading strategy to a trader based on the trader's risk tolerance and other considerations such as the horizon over which the trade is to be completed. In order to meet these needs and to overcome deficiencies in the field, the present invention enables portfolio traders to forecast the transaction costs of a proposed trade execution based on a user-selected trading style and inputs pertaining to order characteristics and trade difficulty. The invention also provides an optimized trading strategy to satisfy user-defined constraints.